In order to illustrate these ideas, we will consider the Lieb-Liniger model [1]} (which can be viewed as a quantum nonlinear Schrödinger equation [2]}). This is a system of \(N\)  bosons with repulsive delta interactions described by the Hamiltonian
\(\hat{H}_\text{LL} = -\frac{1}{2}\sum _{i=1}^{N} \frac{\partial ^2}{\partial x_i^2} + 2c\sum _{i>j} \delta (x_i-x_j) \; ,\) 
